{
  "id": "1709.07746",
  "version": "v1",
  "published": "2017-09-22T13:48:43.000Z",
  "updated": "2017-09-22T13:48:43.000Z",
  "title": "Control of blow-up singularities for nonlinear wave equations",
  "authors": [
    "Satyanad Kichenassamy"
  ],
  "journal": "Evolution Equations and Control Theory, vol. 2, no. 4 (Dec. 2013) 667-677",
  "doi": "10.3934/eect.2013.2.669",
  "categories": [
    "math.AP",
    "nlin.PS"
  ],
  "abstract": "While the global boundary control of nonlinear wave equations that exhibit blow-up is generally impossible, we show on a typical example, motivated by laser breakdown, that it is possible to control solutions with small data so that they blow up on a prescribed compact set bounded away from the boundary of the domain. This is achieved using the representation of singular solutions with prescribed blow-up surface given by Fuchsian reduction. We outline on this example simple methods that may be of wider applicability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-22T13:48:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93B05",
      "93C20",
      "35L71"
    ],
    "keywords": [
      "nonlinear wave equations",
      "blow-up singularities",
      "prescribed compact set bounded away",
      "example simple methods",
      "global boundary control"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}